The last vendor I would imagine getting into online storage is Microsoft. But Redmond is always full of surprises (some more nightmarish than others), and have recently opened up a small beta for an online storage system, giving 500MB of “accessible from anywhere” storage to a select 5,000 people.
This new service, dubbed Windows Live Folders, isn't new to the market. Many other companies offer great amounts of storage, though Microsoft may definitely be able to one-up them when it comes to Windows integration. Until the beta is more publically available, though, we won't know. Microsoft plans to open it up to a wider market within a few months.
Online storage is something that has come and gone over the years. In the earlier days of the Internet, many startup companies offering 10 to 50 to 100MB began popping up here and there, touting it as the next phase in storage. While it has still not quite caught on, many companies (Microsoft and Google included) are pushing for virtual desktops and web applications, which might make online storage more viable.
For a typical desktop user, however, the cost of storage per GB today is so incredibly cheap that I just don't see it taking off. On the other hand, for people that rely a lot on public computers, it can prove very useful. More power to them if they want to give it a stab.